1929 Colonial with the original marble tiles/mesh/mortar base in the only full bath. The project this summer is to remove all of it and start fresh.

The issue, per se: perpendicularly, on top of the joists, the builder laid 3/4" pine, then the mortar/mesh and tiles. That combo extends only 2" or so under the facing edge of the tub. To support the body of the old tub, he laid 2x4s across the joists. Okay, doesn't sound great, but it's held up so far!

My question(s)- after I pull the old flooring and sister up the joists to get them higher/closer to the proper level, what's the proper procedure? I know to lay 3/4" plywood and I know I need backer board. But I've read that I need a waterproof membrane OR visqueenon top of the plywood. Which one?

I've read that I should adhere the backerboard with mortar OR screws/nails. Which?

Finally, since I have to pull the tub, should I tile under it, too? It's more work, but I guess I'm worried about watertight integrity.

Any help is greatly appreciated, since my lovely spouse thinks I know everything...